Circular Edge Dislocation Research Articles

Polarization Properties of Partially Coherent Circular Edge Dislocation Beams in Biological Tissue

Polarization Properties of Partially Coherent Circular Edge Dislocation Beams in Biological Tissue

Coherence and polarization behaviors of partially coherent circular edge dislocation beam in biological tissue

The effects of the several factors on the changes in spectral degree of polarization P(ρ,-ρ,z) and spectral degree of coherence μ(ρ,-ρ,z), μ(ρ,0,z) for the partially coherent circular edge dislocation beam propagating in biological tissue have been studied. It is shown that both beam wavelength λ and dislocation number n have no effect on the initial values of the three, while the values of field points distance ρx and spatial self-correlation length σyy play a significant role. During the propagation, the curves of P(ρ,-ρ,z), μ(ρ,-ρ,z) and μ(ρ,0,z) with different beam parameters will undergo different fluctuation, eventually the former tends to be a certain value less than its initial one and the latter two tend to zero. The smaller ρx is, the higher the coherence of the beam is. The visible light is more suitable for biological tissue disease diagnosis compared to the far infrared and ultraviolet light. The beam with larger n will possess more richer optical distribution when propagating in biological tissues. The difference value between σyy and σxx will significantly influence the change range of P(ρ,-ρ,z), μ(ρ,-ρ,z) and μ(ρ,0,z).

Abruptly dual auto-focusing circle Pearcey edge dislocation beams

In this manuscript, a new, to the best of our knowledge, type of abruptly dual auto-focusing and self-healing beam constructed by nesting a circular edge dislocation (CED) in a circle Pearcey beam (CPB) is introduced theoretically and demonstrated experimentally. The circle Pearcey edge dislocation beam (CPEDB) is endowed with the abruptly dual auto-focusing property and the ability of self-healing superior to that of the CPB. One can adjust not only the focal length, the intensity and the abruptness of the dual foci but also the radius of the CED of the CPEDB by setting proper parameters, making it a more applicable candidate than conventional abruptly auto-focusing beams for applications such as biomedical treatment and laser ablation. And we use the similarity, the structural similarity and the mean squared error indexes to quantify the ability of self-healing of the CPEDB, which is found to be superior to that of the CPB. Moreover, the nested CED is investigated, whose proportion and rate of the collapse are both tunable. This beam is promising in applications such as trapping microparticles and optical manipulation.

Interaction of Two Coaxial Penny-Shaped Cracks Near an Arbitrarily Graded Interface in Functionally Graded Materials: Exact and Approximate Solutions

Abstract Multiple cracks interaction is an important topic in fracture mechanics. The related solutions are helpful to understand the failure process and the toughening mechanism of brittle materials. Previous works on the topic were most for homogenous material. In this paper, we extend the analysis and examine the problem of interaction of two coaxial penny-shaped cracks near an arbitrarily graded interface in functionally graded materials (FGMs). The cracks are modelled as circular edge dislocation loops. An efficient dislocation solution for FGMs and Fredholm integral equation technique are used to solve the crack problem. Both exact solution using a system of integral equations and approximate solution by virtue of Kachanov’s method are presented. Unlike most existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, i.e., graded shear modulus according to special functions and constant Poisson’s ratio, the present method is more flexible since it can consider arbitrarily graded shear modulus and Poisson’s ratio. The validity of the present solutions is checked by comparing to existing results in literatures for two stacked penny-shaped cracks in homogenous material and a penny-shaped crack near a graded interface with exponentially graded shear modulus. Finally, a practical example of double cracks interaction in a real epoxy-glass FGM with measured data of material properties is considered. The error due to the assumption of special gradation is also discussed.

Comparison of propagation properties of circular edge dislocation beams and circular−linear edge dislocation beams

In this study, based on the extended Huygens–Fresnel principle, the propagation expressions of circular edge dislocation beams and circular–linear edge dislocation beams were obtained. The propagation properties of the two types of beam were compared in free space and atmospheric turbulence. The results show that, when circular–linear edge dislocation beams propagate in free space or atmospheric turbulence, because the linear edge dislocation is located in different beam locations, circular edge dislocation vanishes or evolves into a pair of optical vortices. However, when circular edge dislocation beams propagate in space, circular edge dislocation exists stably in free space propagation, while it evolves into a pair of optical vortices in atmospheric turbulence propagation. Therefore, the propagation properties of circular edge dislocation can be adjusted by adding linear edge dislocation when circular edge dislocation beams propagate through free space and atmospheric turbulence. This research can be useful for applications in optical communications.

Splitting of an edge dislocation by a vortex emergent from a nonparaxial beam

The splitting of a linear or circular edge dislocation by a vortex nested in a nonparaxial Gaussian beam is studied. It is found that the edge dislocations are unstable and vanish, while new vortices may take place and the total topological charge may change with propagation. The location of the vortex, the intercept and slope of the edge dislocation, or the location and radius of the circular edge dislocation in the initial beam may affect the number and positions of vortices occurring in the field. The results are compared with previous works.

On the interaction of solute atoms with circular inhomogeneity and edge dislocation

A two-dimensional elastic solution for the stress field of a line dilatation near a circular inhomogeneity is obtained. A line dilatation is used to represent a row of solute atoms, referred to as a solute rod. The image effect is investigated with an especial attention. It is shown that a soft inhomogeneity attracts solute rods and a hard inhomogeneity repels solute rods. Based on this, the interactions of solute atoms with inhomogeneity-edge dislocation are studied by inserting more solute atoms into the matrix one-by-one, with an especial focus on the distribution of solute atoms (rods) around inhomogeneity and edge dislocation. As two typical applications of the present method, two simple cases are analyzed in details, with the inhomogeneity considered as a nano-void and a hard nano-fiber, respectively. It is shown that the equilibrium concentration distribution of solutes near an inhomogeneity is non-local, which not only depends on the local hydrostatic stress but also on the hydrostatic stress in the adjacent region. Besides, the shear stress on an edge dislocation, generated by hydrogen atmospheres between a circular nano-void/fiber and the dislocation, is calculated numerically. The results show that the hydrogen atmosphere around dislocations can shield the long-range elastic interaction between dislocations and other internal stress sources, supporting the so-called hydrogen enhanced localized plasticity.

Propagation of Correlation Singularities of a Partially Coherent Laguerre–Gaussian Electromagnetic Beam in a Uniaxial Crystal

The correlation singularities of a partially coherent Laguerre–Gaussian (LG) electromagnetic beam in a uniaxial crystal is shown to possess interesting evolution behavior. The analytical formula for the cross-spectral density matrix of a partially coherent LG electromagnetic beam propagating in a uniaxial crystal orthogonal to the optical axis is derived. It is found that the correlation singularities of a partially coherent LG electromagnetic beam in a uniaxial crystal is closely determined by the spatial coherence and mode orders of the beam, and the refractive indexes of the crystal. For a partially coherent LG electromagnetic beam, the correlation singularities can propagate further in a uniaxial crystal than that in isotropic medium. For a fully coherent LG electromagnetic beam, in isotropic medium the central correlation singularities and circular edge dislocations persist upon propagation; in a uniaxial crystal the circular edge dislocations become imperfect, and the central correlation singularities with topological charges $l \ne 1$ split up into correlation singularities with topological charges equaling 1.

Trapping two types of particles using a focused partially coherent circular edge dislocations beam

A focused partially coherent circular edge dislocations beam used to trap Rayleigh dielectric sphere with different refractive indices is studied. The dependence of radiation forces on the number of circular edge dislocations p, the spatial correlation length σ0, relative refractive index nr, and particle radius a are analyzed and illustrated by numerical examples. It is shown that the focused partially coherent circular edge dislocations beam can be used to trap high index of refraction particles at focus F and bright ring R2, and simultaneously to capture low index of refraction particles at dark ring R1. It is much easier to capture the high index of refraction particles at focus F and the low index of refraction particles at dark ring as for the larger number of circular edge dislocations p and the spatial correlation length σ0, therefore it is necessary to optimally choose on p and σ0 for obtaining an optimal optical guiding. The ranges of the radius for two types of particles stably captured also have been determined. The obtained results are useful for analyzing the trapping efficiency of circular edge dislocations beams applied in micromanipulation technology.

Dynamic evolution of circular edge dislocations in free space and atmospheric turbulence.

Based on the extended Huygens-Fresnel principle, the analytical expressions for the cross-spectral density function of circular edge dislocation beams propagating through atmospheric turbulence and free space have been derived, and used to study the dynamic evolution of circular edge dislocations. It is shown that the number of circular edge dislocations on propagation equals that at the source plane when propagating through free space. The radius of circular edge dislocations increases with increasing propagation distance z. n-circular edge dislocations vanish and transform to n pairs of optical vortices with the opposite topological charge when propagating through atmospheric turbulence, and the position of each pair of optical vortices are symmetric about the slanted axis y = x. All the optical vortices will annihilate as soon as the propagation distance becomes large enough. The smaller radius of circular edge dislocation corresponds with the sooner annihilation of optical vortices. The structure constant affects the annihilation distance of the pairs of optical vortices, and the annihilation distance of the pairs of optical vortices will increase with the decrement of the structure constant.

Propagation of Riemann–Silberstein vortices through an astigmatic lens

The propagation of Riemann-Silberstein (RS) vortices for Gaussian vortex beams with topological charges m=+1 through a lens is studied. It is shown that if there is an ideal lens, a RS vortex and a circular edge dislocation appear for Gaussian on-axis vortex beams, while only RS vortices take place for Gaussian off-axis vortex beams. In the presence of an astigmatic lens, there exist RS vortices but no edge dislocations for both Gaussian on-axis and off-axis beams. By varying the astigmatic coefficient, the off-axis parameter, and the propagation distance, the motion, creation, and annihilation of vortices may take place, and in the process, the total topological charge of RS vortices remains unchanged.

Dynamic evolution of Riemann–Silberstein vortices for Gaussian vortex beams

The dynamic evolution of Riemann–Silberstein (RS) vortices for Gaussian vortex beams with topological charges m = ± 1 in free space is studied. It is shown that for Gaussian on-axis vortex beams there exist both RS vortex with m = + 2 and circular edge dislocation. For Gaussian off-axis vortex beams the circular edge dislocation splits into two RS vortices with opposite topological charges m = ± 1 and the RS vortex with m = + 2 decays into two vortices with same topological charges m = + 1. The motion of RS vortices takes place by varying the propagation distance, waist width, off-axis parameter, or topological charge. RS vortices for Gaussian vortex-free beams can be treated as a special case. The results are illustrated analytically and numerically.

Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams

Phase singularities and spectral changes of spectrally partially coherent higher-order Bessel-Gauss pulsed beams in free-space propagation are studied, and the analytical expressions for the spectral degree of coherence and spectrum are derived. It is shown that there always exists an optical vortex at the center of the beam and the topological charge is conserved during the propagation. Some circular edge dislocations appear and the spectrum changes on propagation. A rapid spectral transition takes place. Numerical illustrative examples are given and the results are explained physically.

Distribution of phase and orbital angular momentum of tightly focused vortex beams

Based on vectorial Debye theory, the expressions for the distribution of the light field and orbital angular momentum (OAM) of tightly focused vortex beams have been derived. A Bessel-Gaussian (BG) beam is set as the model of the vortex beam. The phase distribution of the field component in the x direction near focus is analyzed as usual by presenting phase contours. It is found that circular edge dislocations exist in the focal plane, but they evolve as screw wavefront dislocations in observation planes away from the focus. Moreover, the dependence of the distribution of phase contours and OAM in the focal plane on the numerical aperture is shown. The distribution of OAM along the z axis is studied; it is found that the optimal location for applications of OAM of vortex beams along the z axis is near the focal plane.

Coherence vortices in partially coherent beams consisting of a superposition of Laguerre-Gaussian modes

The coherence vortices in a new class of partially coherent beams with separable phase recently proposed by Bogatyryova et al. are studied in detail. The new beams are generated by taking an incoherent superposition of Laguerre-Gaussian (LG) modes with equal azimuthal index. It is shown that the mode indices and weight factors of superposed LG modes, as well as the reference choice, affect the position where the circular edge dislocation takes place, and result in the vortex disappearance or the appearance of more than one coherence vortices. Furthermore, there also exist coherence vortices in partially coherent beams with non-separable phase consisting of an incoherent superposition of LG modes.

Vortex revivals with trapped light

We predict that vortex dipoles nested in light beams trapped in graded-index media can undergo closed Berry trajectories, yielding periodic vortex annihilations and revivals along the light-propagation direction. The vortex revivals from vortex-free wave fronts are mediated by Freund stationary point bundles that carry the necessary Poincaré-Hopf indices. Vortex spiraling and spontaneous generation of circular-edge dislocations are also found to occur.

Laser-Induced Nonlinear Gaussian Lens in Liquid Crystal Cell Gives Birth to Optical Vortices

For the first time we report the study of self-induced nonlinear lens in a liquid crystal cell with azo dye and the phase dislocations on a wave front of the beam passing through the lens. Depending on the experimental conditions, circular edge dislocation or optical vortices pairs may be created on the wave front.

The Gaussian lenses give birth to optical vortices in laser beams

It is shown theoretically that Gaussian-like lenses initiate birth, evolution and annihilation of the phase singularities in coherent beams with initially smooth wavefront. The stigmatic lens originates circular edge dislocation, which disappears immediately. The astigmatic Gaussian lenses give birth to quadrupoles of opposite single-charged optical vortices. The optical vortices move in space along a closed trajectory, the more stretched the greater is the lens astigmatism. The developed model gives the complete scenario of the optical singularities origin and evolution, and describes naturally all experimentally observed features for known light-induced Gaussian-like nonlinear lenses.

Elastic fields of a dislocation loop near a stress-free surface

The displacement field around a finite circular edge dislocation loop lying parallel to a stress-free surface has been calculated. The results indicate that when the loop is located close to the free surface the displacement field is extremely asymmetric across the loop plane. This influences the elastic interaction between the loop and point defects. The free-surface effect is significant for loops located within about five times the loop radius from the free surface.

The application of weak‐beam imaging to studies of small dislocational loops

SUMMARYCoupled differential equations for calculating diffracted ands tranmitted intensities from thin crystals have been solved numerically for many beam diffracting conditions. This approach has been used to enable us to study weak‐beam dark‐field images from small circular edge dislocation loops. The exact displacement field around such loops has been calculated using isotropic elasticity theory. Crystal orientations have been chosen to obtain single systematic rows of low order reflections and loop images have been calculated for different combinations of strong and weak beams. Although emphasis has been placed on investigating the application of weak beam imaging to determine the nature of small loops (diam. < 10 nm) a preliminary study has also been made of g.b = 0 residual images. The calculated images have been compared with experimental weak beam images of small loops in neutron irradiated molybdenum.